Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.
It might be tempting to declare that your shipment is a lower freight class than it actually is in order to secure a lower price, however, carriers will re-classify your freight for accuracy and charge you a fee for having to do so.
Yes. If your shipment can be stacked, it allows the carrier to fit more freight into their truck.